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Ernst Schröder's important work is in the area of algebra, set theory and logic. He studied under Hesse and Kirchhoff then under Franz Neumann. His work on ordered sets and ordinal numbers is fundamental to the subject.
In 1877 in Der Operationskreis des Logikkalkuls Schröder, influenced by Boole and Grassmann, emphasised the duality of conjunction (intersection) and disjunction (union) showing how dual theorems could be found. He seems to be the first to use the term mathematical logic and he compares algebra and Boole's logic saying:-
There is certainly a contrast of the objects of the two operations. They are totally different. In arithmetic, letters are numbers, but here, they are arbitrary concepts.
In Vorlesungen über die Algebra der Logik, a large work published between 1890 and 1905 (it was completed by E. Müller after his death), Schröder gave a detailed account of algebraic logic, provided a source for Tarski to develop the modern algebraic theory and gave an extensive bibliography of the history of logic. Lattice theory also grew out of this work.
In addition to his work on logic he wrote an important article Über iterirte Functionen (1871) often cited as a basis of modern dynamical systems theory.
Article by: J J O'Connor and E F Robertson
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